Optimization of corrugated horns radiation patterns via a spline-profile Christophe Granet CSIRO Telecommunications & Industrial Physics PO Box 76, Epping 1710, NSW, Australia 1. Introduction Corrugated horns are widely used as feeds for reflector antennas [1] or as direct radiators, as in global earth illumination from a satellite [2] [3] or source antenna in an anechoic chamber. Shaping the radiation pattern of a corrugated horn is mainly done by shaping the profile [4-6], and to a lesser extent, for wide-band applications, by using a mode-converter [7-9] tuned to the design frequency. In the literature, the profile of corrugated horns is optimised either by using known information on the effect of conventional profiles [4] or by combining some of these profiles [5,6]. Some authors report successful optimisation [10,11] using as parameters the profile and/or slot-depths of each corrugation. In this paper, we define the profile of a corrugated horn as a spline and optimise the radiation pattern by shaping the profile. A computer program has been written to optimise the profile to meet a specified radiation pattern. The horn synthesis is based on minimization of a penalty function representing a measure of the extent to which the pattern constraints are violated. The approach is similar to that which has been applied to the synthesis of array feeds for reflectors with gain pattern constraints [12], the only difference in this case being that profile-parameters rather than feed- parameters are the variables to be optimised. The penalty function is of the least th p index form with p set equal to 2. The minimization is done via a quasi-Newton method in which the derivatives are approximated by finite difference. The envelope is supplied by the user as a list of angular points where an upper-bound and a lower-bound for the co-polarised pattern is specified as well as an upper-bound for the cross-polarised pattern (see Fig. 1). 2. Geometry of the horn Our approach is based loosely on the work described in [13], where a smooth-walled horn was optimised to provide the desired radiation pattern by allowing each section to have its radius and length optimised. A cubic spline was then fitted to these points to provide a so-called “serpentine- profile”. Our approach is slightly different. First of all, we want to optimise a corrugated horn. Secondly, only a few points (or nodes) are used along the length of the horn to generate the spline, namely 2 extreme nodes and 5 inner nodes. We have designed an optimisation program that uses the following parameters (see Fig. 2): • i a : input radius, the first extreme node (fixed value) • o a : output radius, the second extreme node • o d : the allowed displacement of the output radius (usually set as ±20% of o a as the required beamwidth of the radiation pattern is known and o a can be estimated [1]) • 5 4 3 2 1 , , , , a a a a a : radii of the 5 inner nodes • 5 4 3 2 1 , , , , d d d d d : the allowed displacements of each of the inner nodes (making 5 4 3 2 1 , , , , a a a a a constrained variables) • 5 4 3 2 1 , , , , L L L L L : the positions of each of the inner-nodes as percentages of the horn’s length (not used as variables in the first release of the program) • number and pitch of the corrugations, pitch-to-width ratio and number of slots in the mode- converter